Methods and apparatus for bandwidth measurement and bandwidth parameter calculation for laser light

ABSTRACT

A bandwidth meter method and apparatus for measuring the bandwidth of a spectrum of light emitted from a laser input to the bandwidth meter is disclosed, which may comprise an optical bandwidth monitor providing a first output representative of a first parameter which is indicative of the bandwidth of the light emitted from the laser and a second output representative of a second parameter which is indicative of the bandwidth of the light emitted from the laser; and, an actual bandwidth calculation apparatus utilizing the first output and the second output as part of a multivariable equation employing predetermined calibration variables specific to the optical bandwidth monitor, to calculate an actual bandwidth parameter. The actual bandwidth parameter may comprise a spectrum full width at some percent of the maximum within the full width of the spectrum of light emitted from the laser (“FWXM”) or a width between two points on the spectrum enclosing some percentage of the energy of the full spectrum of the spectrum of light emitted from the laser (“EX”). The bandwidth monitor may comprise an etalon and the first output is representative of at least one of a width of a fringe of an optical output of the etalon at FWXM or a width between two points on the spectrum enclosing some percentage of the energy of the full spectrum of light emitted from the laser (“EX&#39;”) and the second output is representative of at least one of a second FWX″M or EX′″, where X≠X″ and X′≠X′″. The precomputed calibration variables may be derived from a measurement of the value of the actual bandwidth parameter utilizing a trusted standard, correlated to the occurrence of the first and second outputs for a calibration spectrum. The value of the actual bandwidth parameter is calculated from the equation: estimated actual BW parameter=K*w 1 +L*w 2 +M, where w 1 =the first measured output representative of FWXM or EX′ and w 2  is the second measured output representative of FWX″M or EX′″. The apparatus and method may be implemented in a laser lithography light source and/or in an integrated circuit lithography tool.

RELATED APPLICATIONS

This application is continuation of U.S. patent application Ser. No.10/789,328, filed on Feb. 27, 2004, which is a continuation-in-part ofU.S. patent application Ser. No. 10/615,321, filed on Jul. 7, 2003,entitled OPTICAL BANDWIDTH METER FOR LASER LIGHT, with inventor Rafac,Attorney Docket No. 2003-0004-01 and is also a continuation-in-part ofU.S. application Ser. No. 10/109,223, filed on Jun. 26, 2003, entitledMETHOD AND APPARATUS FOR MEASURING BANDWIDTH OF AN OPTICAL OUTPUT OF ALASER, Attorney Docket No. 2003-0056-01, also with Rafac as an inventor,both assigned to the assignee of the present application, thedisclosures of each of which are hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to the determination of the spectralbandwidth of a laser. More generally the present invention relates tothe accurate estimation of the bandwidth of an optical source usinginterferometric or diffractive instruments (“spectrometers”) whoseimpulse response functions have bandwidth generally comparable to orlarger than that of the source being measured.

BACKGROUND OF THE INVENTION

The output spectrum of a line-narrowed excimer laser light source forDUV lithography is not generally constant in time. While stability hasgreatly improved with advances in technology, neither the bandwidth northe functional form (shape) of the spectrum is perfectly fixed. Theimpact of spectral shape changes on lithographic performance has so farbeen not completely characterized, however, the influence of full-widthat half-maximum (“FWHM”) and 95%-enclosed energy (“I95%” or “E95” orsometimes referred to as “spectral purity”) illumination bandwidths onimage contrast, log-slope, exposure latitude, etc., have been found tobe significant, as discussed in “Contribution of polychromaticillumination to optical proximity effects in the context of Deep-UVlithography”, A. Kroyan, I. Lalovic, N. R. Farrar, Proc. 21st AnnualBACUS Symposium on Photomask Technology and Management, G. T. Dao and B.J. Grenon (Eds), Monterey Calif., SPIE Vol. 4562, pp. 1112-1120, 2002and “Understanding chromatic aberration impacts on lithographicimaging”, K. Lai, I. Lalovic, R. Fair, A. Kroyan, C. Progler, N. R.Farrar, D. Ames, K. Ahmed, J. Microlithography, Microfabrication andMicrosystems, Vol. 2, Issue 2, pp. 105-111, 2003, the disclosures ofwhich are hereby incorporated by reference.

Dependence on the illuminating spectrum arises, e.g., because opticalmaterial constraints at DUV wavelengths make some chromatic aberrationunavoidable in projection lenses for KrF and ArF lithography. Whilechromatic effects can be minimized with a spectrally narrowed lightsource, even sub-picometer broadening of the illumination spectrumcannot be completely ignored, as discussed in “Modeling the effects ofexcimer laser bandwidth on lithographic performance” A. Kroyan, J. J.Bendik, O. Semprez, N. R. Farrar, C. G. Rowan and C. A. Mack, SPIE Vol.4000, Optical Microlithography XIII, pp. 658-664, March 2000, thedisclosure of which is hereby incorporated by reference. The concernbecomes even more pressing as the industry moves to ever-highernumerical aperture settings and lower values of k₁. To guarantee thatthe aerial image properties are maintained within a given processwindow, it is therefore increasingly more important to have trustworthymetrologic feedback from the light source reporting these spectralfigures-of-merit with high accuracy and reliability and stability.Further, in more advanced applications this information can actually beused to control the workings of the light source in some way, so as tostabilize the light source spectrum or otherwise modulate its bandwidth.In such scenarios, the enhanced spectral performance repeatabilityobtained means that generic optical-proximity (OPC) solutions can beimagined that remain effective and consistent over the system lifetime,e.g., including requirements for enhanced ability to strictly controlbandwidth within some range, i.e., below some threshold but also abovesome threshold.

Commonly used bandwidth metrics such as FWHM and E95 are not alwaysaccurate measures of spectral shape, especially when either isconsidered alone. For example, an increase in the energy content of thefar wings of a spectrum can significantly increase the E95 bandwidthvalue, while leaving the FWHM bandwidth value essentially andeffectively unchanged. Other spectral shape changes can, e.g., leave theE95 constant while altering the FWHM, or can, e.g., leave both thesemetrics constant while changing the center-of-energy of the spectrum orother performance-significant parameter of the spectrum. These shapechanges can often go hand-in-hand with, e.g., bandwidth changes, withsignificant consequences for the design of spectral metrology tools andthe performance of systems relying upon their effectiveness in accuratebandwidth estimation, and particularly in systems, which are becomingever more prevalent, where metrology feedback and concomitant controlfunctions are required to be on a pulse by pulse basis at repetitionrates to and exceeding 4000 Hz.

Variations in the detailed shape and bandwidth of ultra-narrow excimerlaser light sources can originate in a variety of physical mechanisms.Some of this variation is technically unavoidable, and a somewhateffective strategy to overcome this in the past has been to design thelight source in a manner that is generally optimized to minimize theeffects of such variation. Even with engineering controls, however,large changes in spectral shape or bandwidth can sometimes occur due toimproper alignment, failure of optical components, or failure to manageimportant process parameters internal to the light source (e.g., lasergas mixture). It is the job of the onboard spectral metrology package tocorrectly identify and accurately report the light source bandwidth sothat it may be used as trustworthy input to the lithographic processcontrol. To illustrate these shape changes, a number of examples oftypical spectral shape variation seen in a Cymer XLA 100 ArF MOPA(Master-Oscillator/Power-Amplifier) light source measured with ahigh-resolution double-pass echelle grating spectrometer are shown inFIGS. 1A-D. This collection is not exhaustive, but is believed to betypical of a light source of the current generation. The data has beennormalized to equal total energy content for a better comparison of thespectral energy distribution, and to better represent the integratedspectral content for an exposure of, e.g., 200 laser pulses.

SUMMARY OF THE INVENTION

A bandwidth meter method and apparatus for measuring the bandwidth of aspectrum of light emitted from a laser input to the bandwidth meter isdisclosed, which may comprise an optical bandwidth monitor providing afirst output representative of a first parameter which is indicative ofthe bandwidth of the light emitted from the laser and a second outputrepresentative of a second parameter which is indicative of thebandwidth of the light emitted from the laser; and, an actual bandwidthcalculation apparatus utilizing the first output and the second outputas part of a multivariable equation employing predetermined calibrationvariables specific to the optical bandwidth monitor, to calculate anactual bandwidth parameter. The actual bandwidth parameter may comprisea spectrum full width at some percent of the maximum within the fullwidth of the spectrum of light emitted from the laser (“FWXM”) or awidth between two points on the spectrum enclosing some percentage ofthe energy of the full spectrum of the spectrum of light emitted fromthe laser (“EX”). The bandwidth monitor may comprise an etalon and thefirst output is representative of at least one of a width of a fringe ofan optical output of the etalon at FWXM or a width between two points onthe spectrum enclosing some percentage of the energy of the fullspectrum of light emitted from the laser (“EX′”) and the second outputis representative of at least one of a second FWX″M or EX′″, where X≠X″and X′≠X′″. The precomputed calibration variables may be derived from ameasurement of the value of the actual bandwidth parameter utilizing atrusted standard, correlated to the occurrence of the first and secondoutputs for a calibration spectrum. The value of the actual bandwidthparameter is calculated from the equation: estimated actual BWparameter=K*w₁+L*w₂+M, where w₁=the first measured output representativeof FWXM or EX′ and w₂ is the second measured output representative ofFWX″M or EX′″. The apparatus and method may be implemented in a laserlithography light source and/or in an integrated circuit lithographytool.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-D show various responses of the bandwidth spectral shape due tothe alteration of certain parameters of laser operation;

FIG. 2 shows an embodiment of a double-pass grating spectrometer;

FIG. 3 shows a spectrometer utilizing the angular dispersion of a singleplane-etalon according to an embodiment of the present invention;

FIG. 4 shows contours of the difference between Voigt source andLorentzian instrument-convolved spectral FWHM bandwidth versus shapeparameters in units of the Lorentzian FWHM bandpass γ;

FIG. 5 shows simulated etalon-spectrometer FWHM fringe contours for˜5000 experimental light source spectra, with two sets shownillustrating the effect of different choices of the etalon FWHM bandpassγ;

FIG. 6 shows how leakage of energy from the near spectral wings broadensthe FWHM of an etalon fringe according to a simulation of a Lorentzianspectrometer with 0.12 pm FWHM bandpass convolved with real light sourcespectra all having identical FWHM bandwidths of 0.11 pm;

FIGS. 7A and B show, respectively, two measured laser spectra withidentical 0.11 pm FWHMs and different E95 bandwidths (I) and theirconvolutions with a Lorentzian instrument function of 0.12 pm FWHMbandwidth, indicating that the convolved fringe widths at variousthresholds are different for the two spectra; the amount of discrepancybeing shown as Δ in (II), which difference is, e.g., the source ofsystematic error for constant-offset and point-slope FWHM models due tospectral shape change, as described in the present application;

FIGS. 8A-C show improvements of a point-slope FWHM estimator model withfringe width measurement at increasing intensity thresholds X %=25%,50%, 75% according to an embodiment of the present invention, utilizing,e.g., a population of ˜5000 sample spectra, e.g., identical to thoseused in connection with FIG. 16;

FIG. 9 shows results of experiments illustrating systematic sensitivityof fringe point-slope model estimations of E95 to spectral shapevariation induced by changes in laser operating conditions, e.g.,including some 3130 measured spectra, with gray squares using fringeFW35% as input and black circloids using fringe FW75%, with two or threedistinct slopes and three distinct intercepts being apparent,corresponding to different spectral-shape subsets of the data;

FIG. 10 shows predictions of E95 using a two intensity-threshold(FW35%+75%) model of a bandwidth equation, showing 3250 spectra from 4separate experiments combined: Group I, normal F₂ concentration withdelayed MOPA timing; Group II, normal F₂ and normal timing; Group III,enriched F₂, also normal F₂ with shortened MOPA timing, with deviationfrom parity better controlled compared to point-slope model of FIG. 9,and with the inset showing the distribution of tracking errors for thespectral population, with a sigma of 12.1 fm, about 4 fm of which can beexplained by the finite signal to noise ratio (“SNR”) of the sourcespectrum.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Example I in FIG. 1A demonstrates the impact of greatly enriching thefluorine concentration of the laser gas in the master-oscillator of aMOPA or the gain medium of a single-oscillator, e.g., an ArF singlechamber light source. With the addition of extra fluorine to the gasmixture at constant total pressure, the bandwidth increases. In thesemeasurements the FWHM was found to stay constant within the precision ofthe measurement as fluorine was enriched to 13% above the initialconcentration. The E95 was not constant, however, but increased by 18%for the same enrichment. This indicates, e.g., a significant change inthe functional form of the spectrum, and not, e.g., simply a rescalingof the wavelength axis. Such a large over-enrichment of the laser gasmix is not typical, but could be representative of a hypotheticalfailure mode of a light source's internal controls, and in any event isindicative of symptomatic changes in bandwidth spectral shape withlesser increases in fluorine content in the laser chamber.

Example II shown in FIG. 1B illustrates, e.g., the effect of an acousticdisturbance, e.g., timed to pass through the electrode gap during laseroscillation. As evidenced by the fact that the wings of the spectrumremain fixed while the central peak of the spectrum flattens and widens,the shape of the spectral profile is seen to change in response to sucha so-called bandwidth resonance peak event. The effect of this shapechange in the spectral shape is opposite to that of the previous exampleof FIG. 1A. In this case the FWHM bandwidth increased by 52% over thenominal value obtained away from the time-of-flight (“TOF”) resonance,otherwise known as acoustic resonance, while the E95 only rose 8% beyondthe nominal value. The size of the TOF resonance effect can be greatlyreduced with careful discharge chamber designs, but is present to somedegree in all high-repetition rate systems and can occur randomly atdiffering operating laser discharge and output pulse repetition rates,temperatures and other parameters of laser operation.

Example III shown in FIG. 1C illustrates a change due to a very largestatic error in the relative timing of the discharge onset in the gainmedium between two chambers of a MOPA light source. This phenomenonarises, e.g., because the spectral shape and bandwidth of the MO outputis time-dependent. This behavior is therefore somewhat unique to MOPAsystems (MOPO architectures have a further spectral complication due togain competition between the injected and free-running modes of thepower oscillator). In normal operation, the delay between firing of thetwo chambers is chosen to be that time π₀ corresponding to the peak ofMOPA-system electrical-to-optical conversion efficiency. In thismeasurement of shape versus time delay, the bandwidth decreased by about10% in FWHM and 25% in E95 when the delay was increased to λ₀+10 ns.When the delay was decreased to π₀−10 ns, the bandwidth was seen toincrease by approximately the same amount. Changing this delay can beused to control the bandwidth in a MOPA configuration, but such largeoffsets from the efficiency peak introduce trade-offs againstcontrolling other properties of the laser output. This result alsoserves to further illustrate that, e.g., there are spectral shapeconsequences for failure of a light source's internal controls.

The final example IV in FIG. 1D shows the response of the laser spectrumto, e.g., an exaggerated wavefront curvature, e.g., inside the resonatorof a grating-narrowed laser oscillator (MO or single-chamberoscillator). In this experiment, e.g., the surface figure of areflecting optic inside the line-narrowing subsystem was artificiallydistorted by application of mechanical force to simulate the effects ofa defective component inside the laser cavity. The effect on spectralshape was quite profound, as can be seen in the figure. This is a secondexample where the FWHM was altered very little by the shape change, butthe E95 changed by nearly a third. The symmetry of the spectrum was alsodestroyed by this perturbation. This kind of variation is not normal fora well-designed light source, but has been observed to manifest itself,e.g., with a defective or failing optic due, e.g., to excessive thermalloading, differential thermal expansion between a reflecting optic andits mounting, etc.

These four illustrations cover the dominant types of spectral shapevariation seen in research and development efforts ongoing at applicantsassignee. They are but illustrative of types of spectral changes thatcan and do quite often occur which can result in erroneous metrology,which can, e.g., report bandwidth within specifications, whatever arechosen for the specifications, when the actual bandwidth is not inspecification and out of specification when the actual bandwidth is notout of specification. Either case is detrimental to laser operation inthe very high repetition rate tightly controlled wavelength/bandwidth,bandwidth stability, dose stability and other stringent operatingparameter measurement and control requirements. The challenge is todevelop metrology on-board or external to the light source that does notfail to account for the spectral changes that could negatively impactlithographic performance of the illuminated exposure tool, and to dothis accurately in spite of, e.g., changes in the functional form orshape of the spectrum.

Many examples exist of bandwidth measurement and estimation techniquesfor DUV light sources. However, the development of accurate and robustspectral metrology on a per-pulse basis for a high repetition-rateexcimer laser source is very technically challenging and at least muchmore technically challenging than may heretofore have been appreciatedin prior art metrology systems. For future-generation light sources, anideal spectral metrology solution would have most, if not all, of thefollowing five features. The solution may require, e.g., very highspectroscopic resolution, which can be recast more rigorously, e.g., byrequiring that the impulse response (instrument function) of thespectrometer should have a bandwidth many times smaller than that of thelight source spectrum. The solution may also require, e.g., wideinspection range in wavelength (λ) space. It has been suggested thateven small changes in the far wings of the illumination spectrum cansignificantly impact the aerial image properties; this requirement issimilarly necessary for direct computation of E95, as discussed, e.g.,in “Effects of 95% integral vs. FWHM bandwidth specifications onlithographic imaging”, A. Kroyan, I. Lalovic and N. R. Farrar, SPIE Vol.4346, Optical Microlithography XIV, pp. 1244-1253, March 2001, thedisclosure of which is hereby incorporated by reference. The solutionmay also require, e.g., an accurate and robust method for disentangling(deconvolving) the bandwidth of the source spectrum from the instrumentfunction of the spectrometer, which in general is non-negligible toassuring proper measurements and is becoming increasingly more critical.This could, e.g., either be a direct deconvolution using an independentmeasurement of the instrument function, or some sort of mathematical orsemi-empirical model, e.g., that obtains a similar result or estimate.The solution may also require, e.g., a high signal-to-noise ratio(“SNR”) for a single-pulse measurement. Ideally, e.g., this is requiredfor per-pulse assessment of spectral quality and lithographic processjudgment. The system may also require, e.g., optical and mechanicalsimplicity and robustness, which can be necessary, e.g., for stabilityof calibration, repeatability of measurement, and long-life in, e.g., alithography production environment.

It may be difficult (if not impossible) to simultaneously satisfy all ofthese requirements with current technology. Multi-pass gratingspectrometers, e.g., as shown in FIG. 2 can provide excellentspectroscopic resolution, wide inspection ranges, and ability todeconvolve the influence of the instrument function using Fourier orother methods. As shown in FIG. 2, such a spectrometer 20 may include,e.g., an entrance slit 22, a grating 24, and a maximum reflectivitymirror 26, along with a spectral intensity detector 30. However, suchinstruments are bulky, fragile, generally require moving parts fortuning, and can be hard to install, align, calibrate and maintain.Because of their low acceptance, high-resolution grating spectrometersalso require long exposures for an adequate (“SNR”), rendering themimpractical for per-pulse reporting of spectral quality. They are alsoexpensive, commanding prices that may reach a significant fraction ofthe total outlay for a high-performance light source, e.g., a laserlithography tool light source. Grating spectrometers are indispensabletools for system qualification and in research roles where very finedetails of spectral shape and out-of-band energy distribution must beaccurately characterized in terms of spectral purity, line asymmetry,etc. They are not generally practical, however, for onboard real-timewavelength or bandwidth metrology measurements, e.g., in lithographyproduction applications.

Fabry-Perot etalon spectrometers, e.g., as shown in FIG. 3 can providean alternative solution. They are optically simple and can be mademechanically robust with no moving parts. Such a spectrometer 40, asshown in FIG. 4 may include, e.g., a beam homoginizer 42, a collimatinglens 44, an etalon 465, an imaging lens 50 and an intensity detectory52, which may include, e.g., a lateral photo-diode array 54. The lack ofnecessity for a slit means that for a given input, a large irradiancecan be obtained in the detector plane, e.g., at the PDA 54, e.g., evenin spite of poor beam quality. Because of this a plane-mirror etalon 46can capture useful spectral information from a single short pulse ofillumination by utilizing the angular discrimination between transmittedbeams at different wavelengths.

To compete with grating spectrometers purely on the basis ofspectroscopic resolution and inspection interval, long free spectralrange (“FSR”), high transmission, and high-finesse (ℑ) etalons arerequired. A commercial double-pass echelle grating spectrometer for usein a DUV light source might achieve a fixed inspection range of 15 pmand an instrument function of 50 fm FWHM bandpass when operating in highorder. To match this performance with an etalon spectrometer, an FSR≈15pm and a finesse of ℑ≈300 would be required. While this kind ofperformance is routinely surpassed for longer wavelengths, it is notpractical in the DUV, where surface figure (parallelism, flatness,roughness) and mirror coating limitations typically limit the totalfinesse to ℑ<50. The finesse-loss due to geometric imperfections can bereduced by using a spherical-confocal etalon that is mode-degenerate,because the focusing effect of the spherical mirrors results in a modediameter that is small on the mirror surface thereby suppressing theinfluence of geometric imperfections. Unfortunately, in thisconfiguration the inter-mirror optical path length must be scanned forspectral analysis, which can make analysis of isolated short pulses oreven of a few pulses in a burst of pulses impractical. Further, for agiven spacing the FSR is halved using this method, and the mode-matchingrequirement also means that, e.g., the insertion loss can beprohibitively high for beams of poor quality. Therefore, the confocalarrangement discards many of the special advantages of the etalonspectrometer 40 in trying to obtain grating spectrometer-likeperformance. A similar conclusion obtains for other schemes that obtainhigh spectroscopic resolution and large inspection ranges with seriesarrangements of multiple etalons.

In spite of these limitations, air-spaced plane-etalon spectrometers areoften the best choice for numerous spectral measurement tasks. While notoffering the largest inspection ranges or resolving powers in the DUV,reasonable compromises can be reached in these areas while retaining thedesired features, e.g., superior single-short-pulse SNRs andadaptability to manufacturing applications that require physicalrobustness and reliability. For spectral monitoring, e.g., oflithographic tool illumination, plane etalons with FSRs from 2 to 40 pmattaining finesse values from 20-50 can be employed. This means thatthese devices are used in a regime where the ratio of the FWHM bandwidthof the spectrometer instrument function to the bandwidth of the lightsource spectrum is close to or greater than unity. In this regime, theetalon FWHM fringe width, as discussed above, has been shown to havenon-negligible sensitivity to details of the source spectral shape otherthan its FWHM, including, e.g., the spectral purity, i.e., the amount ofintegrated energy within some area of the spectrum on either side of thepeak wavelength, usually measured as E 95% or E95, with the spectralpurity increasing as the width of, e.g., E95 decreases.

As was discussed above the spectral shape of DUV light sources may varysignificantly, particularly in cases of defective components orcontrols. These shape changes may “hide” beneath the instrument functionof the spectrometer and influence its output. Therefore, applicant hasdetermined that special emphasis must be placed on the third requirementlisted above, namely, that the method used to estimate the bandwidth ofthe source spectrum from the etalon fringe measurement be dependable andfree from systematic error caused by changes in the shape of the sourcespectrum.

Consideration must be had of the impact of spectral shape on estimationof source light bandwidth. A number of techniques can be applied torecover the complete source spectrum or source bandwidth from aspectrometer measurement. The signal output O(λ) by the spectrometer isthe convolution of the source spectrum S(λ) and the instrument functionof the spectrometer I(λ): $\begin{matrix}{{O(\lambda)} = {\int_{- \infty}^{\infty}{{S(\Lambda)}{I( {\lambda - \Lambda} )}\quad{\mathbb{d}\Lambda}}}} & (1)\end{matrix}$

Three methods are commonly employed to determine the bandwidth of asource spectrum S(λ) given the spectrometer signal O(λ). It will beunderstood by those skilled in the art that the output signal may be,e.g., the result of the detection of fringes, e.g., from the opticaloutput of an etalon by the use, e.g., of a photo-diode array (“PDA”)which may detect, e.g., the intensity distribution of light laterallyacross the diodes of the array. Such intensity values may then be usedto produce a plot of the intensities, which mathematically, using, e.g.,interpolative techniques can be used, e.g., by a digital processor tocompute the location in the array of intensities amounting to, e.g., aFWHM or a FW75% M or FW35% M, as examples and/or the positions in thearray of intensities that constitute the bounds of an E95 value, or anE75 value, or the like. Therefore, the output signal of the detector inthe form of an array of intensities of light distributed, e.g., along alinear arrangement of photo-diodes, is converted to another signalrepresentative of a value derived from the bandwidth detector outputfunction O(X), which the overall system utilizes as the measurement of,e.g., FWHM or E95 or the like. This is one form of an output from thebandwidth detector that is representative of a parameter that in turn isrepresentative of the actual bandwidth of the light source, i.e.,representative of the actual FWHM or E95.

The most complete of the commonly applied methods is a fulldeconvolution of the signal O(λ). Given O(λ) and an independentdetermination of I(λ), a solution to Equation 1 can be found, e.g.,using Fourier or other methods. This can be a challenging task, however,because in general there are many source spectra S(λ) that convolve withI(λ) to give the same actual output signal O(λ), which is the completeO(λ), only discrete portions of which the bandwidth detector imager,i.e., PDA, actually “sees” and from which the values of therepresentative parameters, e.g., FWHM or E95 are calculated by thebandwidth detector system.

Usually special efforts must be made to deal with noise in themeasurements and zeros in I(λ), and for a fine-grained spectrum thisprocess can take a considerably amount of processing time. For these andother reasons, this method is generally not well suited for monitoringof the bandwidth of a light source spectrum on a per-pulse basis inhigh-repetition rate applications. This method is still preferred whenusing high-resolution grating spectrometer measurements for basicresearch or in light-source manufacturing test environments, where verydetailed knowledge of the average spectrum is required.

A second technique appeals to mathematical arguments made on the basisof analytic approximations of the source spectrum and instrumentfunction. For example, in the cases where the spectral densities S(λ)and I(λ) are both perfectly Lorentzian or both perfectly Gaussian indistribution, the FWHM and E95 bandwidths of the source spectrum S(λ)are very simply related to the bandwidths of O(λ) and I(λ). For example,consider a Lorentzian source spectrum and instrument function with FWHMbandwidths Γ_(S) and Γ_(I), respectively: $\begin{matrix}\begin{matrix}{{{S(\lambda)} = {\frac{1}{\pi}\frac{\Gamma_{S}/2}{( {\lambda - \lambda_{0}} )^{2} + ( {\Gamma_{S}/2} )^{2}}}},} \\{{I(\lambda)} = {\frac{1}{\pi}\frac{\Gamma_{I}/2}{( {\lambda - \lambda_{0}} )^{2} + ( {\Gamma_{I}/2} )^{2}}}} \\{{O(\lambda)} = {{\int_{- \infty}^{\infty}{{S(\Lambda)}{I( {\lambda - \Lambda} )}}}\quad = { {\frac{1}{\pi}\frac{( {\Gamma_{S} + \Gamma_{I}} )/2}{\begin{matrix}{( {\lambda - \lambda_{0}} )^{2} +} \\( {( {\Gamma_{S} + \Gamma_{I}} )/2} )^{2}\end{matrix}}}\Rightarrow\Gamma_{S}  = {\Gamma_{O} - {\Gamma_{I}.}}}}}\end{matrix} & (2)\end{matrix}$Hence, in this case the FWHM bandwidth Γ_(S) of S(λ) is found just bysubtraction of a constant. The E95 value could be handled similarly,because $\begin{matrix}{{{E\lbrack {\frac{1}{\pi}\frac{\Gamma/2}{( {\lambda - \lambda_{0}} )^{2} + ( {\Gamma/2} )^{2}}} \rbrack} = {{\Gamma\quad{\tan( {0.95\frac{\pi}{2}} )}} \approx {12.71\Gamma}}},} & (3)\end{matrix}$where E[ . . . ] denotes the E95 bandwidth of the bracketed spectraldistribution.

A third and widely used method for obtaining the light source bandwidthwithout full deconvolution begins with Equations 2 and 3 as a firstguess, but modifies its form or adds additional corrective terms toreduce the systematic error that results from, e.g., imperfectassumptions about the shape of the source spectrum and/or instrumentfunction. It is therefore semi-empirical in character and requirescalibration against a trusted measurement. In a typical scenario thelight source is run through some series of operating modes or conditionsthat cause its bandwidth to vary. The source FWHM bandwidth Γ_(S) iscarefully determined during this test using, e.g., an externalhigh-resolution grating spectrometer and Fourier deconvolution (or bysome other means). At the same time, the output of the metrology systemundergoing calibration is recorded. As noted above, this output can be,e.g., the FWHM fringe width w of an etalon spectrometer contained insidethe light source, or some digital or analog signal representative of thedetected w. With this data in hand, the source bandwidth Γ_(S) can beestimated from the relation Γ_(S)

f(w). The best choice for the semi-empirical model f can be made frominspection of the data and/or by recourse to mathematical reasoning suchas noted in the just preceding paragraph.

Looking at these semi-empirical models in more detail, the simplestchoice of model, e.g., for FWHM bandwidth estimation is the subtractionof an experimentally determined constant offset:Γ_(S) f(w)=w−δ  (4)This model is mathematically exact, e.g., when both the light sourcespectrum and the instrument function of the spectrometer are purelyLorentzian, as is seen in Equation 2 above. An etalon spectrometer mayhave an instrument function I(λ) that is very nearly Lorentzian, but asillustrated above the spectrum S(λ) of the DUV light source is ingeneral not well approximated by either a Gaussian or Lorentziandistribution, and in fact can be quite difficult to parameterize. Thesimple fact that the ratio E95/FWHM is not constant, as shown, e.g., forthe spectra shown in FIGS. 1A-D, provides a straightforward indicationthat Gaussian or Lorenztian assumptions are inadequate. This ratioremains constant for these analytic forms as can be seen from Equation3, etc. Therefore, the constant offset model (Equation 4) will give animperfect estimate of the source bandwidth Γ_(S), subject to asystematic error dependent on the details of the spectral shape. Toillustrate this point, consider a hypothetical light source the spectrumS_(V)(λ), which is shaped very nearly like a Voigt profile. A Voigtprofile is a convolution of Lorentzian and Gaussian distributions havingequal energy content: $\begin{matrix}{{S_{V}(\lambda)} = {\int_{- \infty}^{\infty}{{\mathbb{d}{\lambda^{\prime}( {\frac{1}{\pi}{\frac{\Gamma_{S}/2}{\begin{matrix}{\lambda^{\prime 2} +} \\( {\Gamma_{S}/2} )^{2}\end{matrix}} \cdot \frac{1}{\sigma\sqrt{2\quad\pi}}}{\exp\lbrack {{- \frac{1}{2}}( \frac{\lambda - \lambda^{\prime}}{\sigma} )^{2}} \rbrack}} )}}.}}} & (5)\end{matrix}$

The source spectral shape is then completely characterized, e.g., by twoparameters, which are the FWHMs Γ_(L) and Γ_(G)=2σ√{square root over (−2ln(½))}2.35σ of the Lorentzian and Gaussian components. The outputO_(V)(λ) of an etalon spectrometer illuminated by this source iswell-approximated by the convolution of S_(V)(λ) with a purelyLorentzian instrument response I_(V)(λ), where the FWHM γ of thisLorenztian is given by the ratio of the etalon FSR to its finesse ℑ:$\begin{matrix}\begin{matrix}{{{O_{V}(\lambda)} = {\int_{- \infty}^{\infty}{\mathbb{d}{\Lambda( {\frac{1}{\pi}{\frac{\gamma/2}{\Lambda^{2} + ( {\gamma/2} )^{2}} \cdot {S_{V}( {\lambda - \Lambda} )}}} )}}}};} \\{\gamma = {\frac{F\quad S\quad R}{\mathfrak{J}}.}}\end{matrix} & (6)\end{matrix}$

FIG. 4 shows the difference between the FWHM of the etalon spectrometeroutput fringe O_(V)(λ) and the FWHM of the source spectrum S_(V)(λ)relative to y as a function of the two independent shape parametersΓ_(L)/γ and Γ_(G)/γ. As Γ_(G)→0, the difference δ between the etalonfringe FWHM and the FWHM of the source spectrum approaches a limitingvalue of γ as expected. This is the condition described by Equation 2.But as the width of the Gaussian component increases, δ gets smaller andthe constant-offset model of Equation 3 will fail to give an accurateestimate of the source bandwidth within current and approaching accuracyand consistency requirements. This discussion is somewhat artificial butillustrates the variation between limiting cases of Lorentzian andGaussian light sources clearly.

Performance of the constant-offset model can be improved by extending itto a point-slope model:Γ_(S) f(w)=w−B  (7)

The point-slope model works well for the hypothetical Voigt spectraldistribution S_(V)(λ), however, only if the parameters Γ_(L) and Γ_(G)are constrained in their variation; for example, if there is a linearrelationship Γ_(G)=mΓ_(L)+b, where m and b are constants, and theoverall bandwidth variation of S_(V)(λ) does not cover too wide a range.However, if the spectral shape is poorly constrained the point-slopemodel can also suffer from inaccuracies, which increasing are becomingintolerable. In the case of FWHM estimation, it is worth again notingthat the performance of these simple models improves greatly when theFWHM bandpass of the instrument function I(λ) is made very small. Asalso discussed above, however, this is difficult or impossible toachieve for plane etalon assemblies of even moderate FSR in the DUV.

A more robust method for estimation of bandwidth using etalonspectrometers will now be discussed. For an arbitrary light sourcespectrum S(λ) it might seem that the only useful bandwidth estimationcan come from rigorous deconvolution of spectra obtained from a devicewith very high spectroscopic resolution. Further, it might seem that E95estimation is even more untenable because it requires integration of thesource spectrum over a wide range of wavelengths. Fortunately, with aclear understanding of the limitations of the technique, robustsemi-empirical methods for bandwidth estimation of both FWHM and E95using relatively wide bandpass etalons may still be obtained. Applicantand his colleagues have studied a number of techniques for estimatingthe bandwidth of, e.g., DUV excimer light source spectra using the widthof etalon fringes as input. By construction, these techniques aredesigned to suppress or actively correct systematic errors that arisedue to spectral shape change. Most of the methods under investigationrely on three simple observations. First, the wider the FWHM bandpassγ=FSR/ℑ of the etalon, the more the fringe FWHM w is influenced byenergy in the wings of the source spectral distribution (and hence itsE95). Second, if the full-width at X % of peak intensity (“FWX %” or“FWXM”) of the fringe is measured, as X→100% the full-width dependsmostly on the energy content near the center of the source spectralline. As X→0%, the full-width depends more on the energy content in thewings of the source spectrum. Third, the space of bandwidths andspectral shapes accessible to a single-oscillator or MOPA light sourceis constrained to a limited range, even in cases of pathologicaloperation or failure of internal components.

With these points in mind, applicant and his colleagues have found intabletop experiments that it is possible to “optimize” the choice ofetalon bandpass γ, the fringe measurement technique, and the bandwidthestimator model to obtain an accurate prediction of the source at somepercentage of the maximum, e.g., FWHM bandwidth, or at some enclosedenergy percentage, e.g., E95 bandwidth, that is relatively immune tosystematic variations in the spectral shape.

Applicant and his colleagues have observed that the FWX % fringe widthw(X %, γ) of an etalon spectrometer with FWHM instrumental bandpass γilluminated by lithography laser light sources is relativelywell-modeled byw(X %,γ)

A(X %,γ)Γ_(source)+B(X %,γ)E_(source)+C(X %,γ),  (8)where A, B, and C are constants that depend on the spectrometerinstrument function and the fraction of intensity at which thefull-width of the fringe is measured, and Γ_(source), E_(source) are theFWHM and E95 of the source spectrum S(γ), respectively, which in part isthe subject of the above referenced patent application Ser. No.10/109,223 by applicant. Equation 8 is a further generalization of themodels discussed herein, taking into account the dependence of thefringe width on the source spectrum. When the ratioE_(source)/Γ_(source)=constant or E_(source)=constant the point-slopemodel obtains, and when either of these conditions hold with A≈1, theconstant-offset model obtains. The coefficients of Equation 8 can bedetermined by computer simulation or calibration against a trustedstandard. In practice, it is helpful to use simulations as a guide inchoosing the parameters X, γ and the functional form of the estimatormodel to obtain the desired sensitivity. The suitability of Equation 8can be judged for a given population of spectral shapes by plotting thefringe width versus the E95 and FWHM of the source spectrum. The modelcan be validated by plots such as that shown in FIG. 5, where the ratioE_(source)/Γ_(source) is not constant over the population but the datastill lie close to a plane in (Γ_(source), E_(source), w)three-dimensional space. This model is not perfect, but appears to holdfor a useful range of (Γ_(source), E_(source), γ) values. Note that aplane also obtains when E_(source)/Γ_(source)=constant, so it isimportant to verify the behavior using a spectral sample that hassignificant variation in this ratio.

For experimentally determined spectral shapes of the kind describedabove, applicant and his colleagues have found that A

B when γ

E_(source) and X=50%. If γ

E_(source)/2

Γ_(source) and X=50%, applicant and his colleagues have found that A

3.5B. This confirms the expectation that as the FWHM of the etaloninstrument function γ narrows, the fringe width w at 50% intensity moreperfectly tracks the source spectral FWHM in spite of shape changes.Applicants have considered the implications of this, namely, if apoint-slope model is used to estimate the FWHM bandwidth of the sourcespectrum from the FWHM of an etalon fringe with too wide a choice of γ,some E95 “bleeds through” the instrument function, as can be seen, e.g.,in FIG. 6. This is because convolution with the instrument functionpulls some energy from the wings of the source spectrum into the core ofthe etalon fringe. If the FWHM (˜core) and E95 (˜wings) of the sourcespectrum vary independently as they are demonstrated to do in thediscussions above, a systematic error can be seen to appear in theestimate of the source FWHM, as illustrated, e.g., in FIGS. 7A and B.

In designing an etalon spectrometer, the available choices of γ=FSR/ℑare highly constrained by the availability of high-quality reflectivecoatings, low-loss/high-flatness substrates, and cavity spacers withvery low wedge angles. Therefore, the optimal choices are not usuallyavailable especially with current generation and future DUV lightsources and with current generation and upcoming lithography toolrequirements. Applicant has discovered, however, that a remedy to thissituation may be found, e.g., by adjusting the threshold parameter X fora given spectral width detection utilized in a new model. The results ofa simulation, e.g., as plotted in FIG. 8 illustrate the effect ofincreasing X from 25% to 50% to 75% of the fringe peak intensity, e.g.,as measured by the bandwidth detector, and forming the bandwidthdetector output, on the error in estimating the FWHM bandwidth of alarge population of source spectra with shape variation, e.g., whenusing a point-slope model and γ

Γ_(source). An improvement appears as X is increased, which applicanthas attributed to a reduction in the sensitivity of the width atincreasing threshold to variation in the balance of energy between thecore and wings of the source spectrum. This can be due, e.g., to thefact the ratio A/B increases as the threshold X increases, because theprocess of convolution with I_(V)(λ) allows less energy from the wingsof the source spectrum to contribute to the FW75% compared to the FW25%.

Applicant has found a direct application of this to metrology, e.g., toE95 metrology. The fact that source spectral E95 variations at constantFWHM can be clearly discerned in the FWX % of an etalon spectrometerfringe, as illustrated, e.g., in FIGS. 6 and 7A and B, indicates, e.g.,that it is possible to estimate the E95 with the required level ofaccuracy and stability of measurement, of a light source spectrum,without recourse to deconvolution and full integral treatment of thedata. In terms of the model (Equation 8), for application of aplane-etalon spectrometer to FWHM estimation it is often sufficient tomake y as small as practical and increase X to the maximum levelpermitted by the angular resolution of the fringe detector, e.g., a PDA,which has a resolution dependant in part on the granularity of pixels(diodes in the array) available for the intensity measurements andtherefore, for such mathematical operations as interpolation. In such acase, A/B can be, e.g., >5 and, e.g., the sensitivity to shape changecan be small enough to be acceptable.

For E95 estimation, however, the situation may still be challengingbecause it may be difficult to construct a scenario where A/B is muchless than unity while still satisfying constraints that originate inother aspects of the spectrometer design (detector resolution and signalto noise, etc.)

Applicant and his colleagues have examined the usefulness of etalonspectrometers for application to metrology, e.g., E95 metrology byexamining the behavior of the FW35% and FW75% fringe widths of anexperimental spectrometer with γ=Max{E_(source)}. This γ was chosen,e.g., because it gives acceptable sensitivity to the energy content inthe wings of the source spectrum without excessively compromising otherperformance aspects. In the experiments, a Cymer XLA 100 prototype laserDUV light source was run over a wide range of conditions within andbeyond its normal operating envelope so as to generate significantvariations in the bandwidth and spectral shape of its output(corresponding to conditions and variations of the types I-III of FIGS.1A-C). The light from this source was homogenized and used to illuminateboth a high-resolution double-pass echelle grating spectrometer and theexperimental etalon spectrometer 40 simultaneously. The gratingspectrometer output was deconvolved using Fourier methods and thecorresponding E95 bandwidths were computed, and the etalon fringepatterns obtained during the grating spectrometer exposure were analyzedand separate fringe values w₁ and w₂, e.g., the fringe FW35% and FW75%values reported. The results are presented in FIG. 9 as a plot of thefringe width at the two intensity thresholds versus the E95 of thedeconvolved source spectrum recorded by the grating spectrometer. Viewedfrom a point-slope perspectiveE_(source)

m·w(X %,γ)+b,  (9)The fringe width follows the source E95 bandwidth change due to, e.g.,MOPA timing offset and fluorine enrichment with one slope m, butresponds with a completely different slope m′≠m against source E95change due to chamber acoustic phenomena, a consequence of the differenttypes of concomitant variation in bandwidth and spectral shapeassociated with different physical processes within the laser. Thebest-fit intercepts b also vary as a function of operating point.Therefore, applicant has concluded from this and other experiments thata full-width measurement at a single intensity threshold X isinsufficient for robust E95 estimation in the presence of shapevariation.

Recognizing that the single-threshold approach is inadequate, applicantand his colleagues considered some other techniques that follow from thefringe width model (Equation 8). In one technique, two etalonspectrometers can be designed so as to obtain sufficiently differentcoefficients A, B, C, for each, as is also the subject of an abovereferenced patent application Ser. No. 10/615,321 in the name ofapplicant. Such spectrometers may be operated simultaneously and inparallel to obtain two different fringe widths; armed with these fringewidths and the set of six coefficients, the system of two multivariablelinear equations may be solved for the unknown source FWHM or E95. Thismethod, however, while potentially very successful in its own right, hasthe cost and complexity disadvantage of requiring two separate etalonspectrometers. Simulations indicate, however, that it can report verygood estimates of both the FWHM and E95 of the source if thecoefficients are chosen properly and certain detection constraints canbe satisfied, as is the subject of the above referenced patentapplication.

An alternative method, according to an embodiment of the presentinvention, that can provide a robust E95 estimate of the source spectrumwhile, e.g., using only a single etalon, applies Equation 8 in adifferent way. In this approach, according to an embodiment of thepresent invention, the etalon bandpass γ is fixed by the finesse andchoice of FSR, but the values of the coefficients A, B, and C can stillbe changed in a significant way by altering the intensity threshold X atwhich the width measurement is performed. For example, for twosufficiently different choices of X, a plane equation can be once againobtained.

To test this embodiment of the present invention, applicant and hiscolleagues repeated the experiments, e.g., with the E95 estimator modelaltered to use, e.g., two intensity thresholds. In this set ofmeasurements, the model chosen was:E_(source)

K·w(35%,γ)+L·w(75%,γ)+M,  (10)where K, L, M are calibration constants determined by the best fit ofthe grating spectrometer measured source spectral E95 to the model. Withthis change, the source E95 estimation accuracy over a wide range ofspectral, shape variations is significantly improved, as can be seen,e.g., by the experimental results, e.g., plotted in FIG. 10. Inaccordance with the model of Equation 8, applicant and his colleaguesbelieve that the combination of, e.g., two FWX % terms partly “senses”independent changes of the source spectral energy distribution in thecore and near wings of the spectral line. This model therefore correctsfor the independent variation of FWHM and E95 to which the simpleone-dimensional (point-slope) model is insensitive. There still remainssome systematic deviation, but the sigma of the error distribution forthe given spectral population was reduced by about a factor of two whenapplying the improved technique according to an embodiment of thepresent invention. Similarly applicant and his colleagues believe thatthe use of two sufficiently separated EX % measurements as the bandwidthdetector output width measurements can have the same effect. The use ofthe two separate and separated X % values for either FW or Emeasurements in the bandwidth detectors can be effective in determiningthe actual bandwidth parameter desired, whether FW or E, e.g., FWHM orE95, depending only on the generation of the appropriate constants K, Land M for a given instrument, e.g., a particular etalon, as describedabove. Similarly, the two measurements with the etalon used forcalibration and later actually sensed, may be one each of the FW and Evariety with the same results.

Also, those skilled in the art will appreciate that with a single widthdetection apparatus, e.g., a PDA, the data needed to process the valuesfor w₁, e.g., a FWXM or an EX′, on the one hand and a w₂, e.g., a FWX″Mor an EX′″, where if both are FW or E, then X≠X″ and X′≠X′″ isavailable. Then the two values of w₁ and w₂ may conveniently andexpeditiously computed simultaneously according to the operation of thedetector and its associated processor from the intensity values obtainedfrom, e.g., the PDA.

While the computation of an energy width (EX %) of the etalonspectrometer fringe for use as an input to a point-slope or other modelcan be more computationally demanding, due, e.g., to the integrationrequired, it is still achievable, and improved computation speeds and/orspecial DSP circuitry, e.g., optimized for the integration task, makethis a viable solution. It may even have certain advantages, however,when it comes to latitude in etalon selection and other aspects of thespectrometer design.

It will also be understood that at best the actual bandwidth parameter,e.g., FWHM or E95, that is the ultimate output of the apparatus andmethod according to the embodiment of the present invention disclosedherein, is only an estimate thereof. It is, however, the actual value sofar as the laser light source and its measurement and control systemsand/or lithography system are concerned. As used in this application,including in the claims, the “actual” value of the bandwidth measurementparameter or the “estimated actual” value are used interchangeably tomean this finally determined value arrived at according to the disclosedembodiments of the present invention and then relied upon by the rest ofthe system as the best and closest determination of the desiredbandwidth measurement parameter, e.g., FWHM or E95, that the system canproduce within the limits discussed herein.

From the above, it will be understood by those skilled in the art thatin spite of a variety of shortcomings, etalon spectrometers havedistinct advantages for application to bandwidth metrology onboardline-narrowed excimer light sources used in DUV lithography. These lightsources have been shown to exhibit dependence of the detailed shape orfunctional form of their output spectra, e.g., due to certain specificoperating conditions. Such shape changes can introduce large systematicerrors into methods commonly used to estimate bandwidth due to thenon-negligible influence of the bandpass of the instrument function ofpractical embodiments of these spectrometers. Fortunately, throughapplication of a simple etalon fringe width model, according to anembodiment of the present invention some special methods that are lesssensitive to these variations are proposed. When used, these techniquescan suppress errors related to spectral shape variation by introducingmeasurement sensitivity to the relative energy distribution between thecore and near wings of the spectrum. Because of the sensitivity of thelithographic process to the illumination bandwidth, management of thissource of systematic error is important to current and futureapplications, particularly those involving active control orstabilization of the source spectrum.

It will also be understood by those skilled in the art that at a moreconceptual level an embodiment of the present invention relates to abandwidth meter method and apparatus that may comprise an opticallydispersive instrument, which may comprise an etalon for example, whichdisperses the energy comprised in the light output of an light source,which may be, e.g., a laser DUV source, or perhaps an EUV light source,e.g., either utilizing a laser produced plasma (“LPP”) or a dischargeproduced plasma (“DPP”). The dispersion converts the output light in itsnatural wavelength domain into a spatial or temporal domain according tothe wavelength distribution of the light energy output from the of thelight source. The invention further contemplates, e.g., a detector,e.g., a photodiode array, that records, respectively, the spatial ortemporal variation of wavelength distribution of the energy, e.g., byutilizing a lateral photodiode array recording light intensities alongthe extent of the array and also may further provide an output signalbased upon the recorded spatial or temporal variation. The output signalmay comprise, e.g., a plurality of widths, e.g., measured between pixelson the array, representative of a spectrum full width at some percent ofthe maximum within the full width of the spectrum of light emitted fromthe light source (“FWXM”) and (“FWX′M”) or a width between two points onthe spectrum defining a content of the spectrum enclosing somepercentage of the energy of the full spectrum of the spectrum of lightemitted from the light source (“EX″”) and (“EX′″”).

An embodiment of the invention further contemplates, e.g., that anycombination of at least two of these values may be used, but that whenthe combination is, e.g., FWXM and FWX′M X≠X′ and when the combinationis, e.g., EX″ and EX′″, X″≠X′″. It will also be understood by thoseskilled in the art that the particular combination used and thedifferences between, e.g., X and X′ or X″ and X′″ may be empiricallyselected according to, e.g., the type of dispersive element, the typeand accuracy (measured, e.g., by SNR) of the recorder and the lightsource, including the types and probabilities of occurrence ofdistortions to the spectra of the light emitted by the light source,e.g., to each be more responsive to different aspects of the energydistribution in the spectra being measured, e.g., to the width at X % ofthe maximum or the width at Y % of the enclosed energy, i.e., generallyspeaking more responsive to the energy in differing parts of thespectra, e.g., the center portion or the skirts (wings) of the spectra.

An embodiment of the invention also contemplates, e.g., the use of afirst calculation apparatus, to calculate the width of the wavelengthdistribution of the energy, respectively, in the space or time domain,based upon, respectively, the spatial or temporal variation of thewavelength distribution of the energy recorded by the detector, i.e., asindicated by the intensity distribution of the light detected by eachphoto-diode (pixel) in the lateral PDA array. This first calculatingdevice, according to an embodiment of the present invention may, e.g.,convert respectively, the spatial or temporal distribution (, e.g., thesensed light intensities in the PDA) into the wavelength domainaccording to the optical properties of the dispersive instrument, i.e.,by determining the above noted width values and output those widthvalues.

According to an embodiment of the present invention a second calculationapparatus, utilizes at least one these width values, representative ofthe wavelength distribution of the energy in the wavelength domain, ascalculated by the first calculation apparatus, and applies them as anargument of a multivariable equation having predetermined calibrationvariables specific to the optical source, the dispersive instrument, thedetector, and the at least one width taken as an argument. That is tosay, as noted above, according to an embodiment of the presentinvention, the predetermined calibration values are determined from theuse of a trusted standard to measure actual wavelength of a spectracorrelated to at least one width output from the particular instrument,e.g., the particular etalon spectrometer such that when that same widthoutput is input to the second calculation apparatus, the use of themultivariable equation with the precomputed calibration variables willreturn the same or essentially the same desired wavelength parameter(FWXM or EX) measured by the trusted standard in the calibrationprocess. An embodiment of the present invention disclosed above relatesto using two such width measurements from the first calculationapparatus, but as here noted, it need only be at least one, and could bemore than two. Also, the first and second calculation apparatus,according to another embodiment of the present invention may be the samecalculation apparatus. The multivariable equation is evaluated tocalculate an actual bandwidth parameter descriptive of the spectraldistribution of the energy output by the light source selected from thegroup FWX*M, EX**.

Those skilled in the art will appreciate that the above-describedembodiments of the invention do not limit the invention to particulardisclosed embodiments. Many changes and modification will be understoodto be available without departing from the scope and content and spiritof the accompanying claims. For example diffractive optic elements thatproduce the required fringe patterns or other bandwidth detectionmeasuring parameters may be utilized besides etalons. Similarly variousmeans are available to arrive at the width measurement values firstcalibrated for and then used in operation, i.e., w₁ (as a function ofsome FWXM or EX and, e.g., an instrument bandpass function) and w₂ (as afunction of some other FWXM or EX and, e.g., the instrument bandpassfunction) for use in the equation of an embodiment of the presentinvention, other than, e.g., the process outputs from a PDA. Inaddition, the final outputs may be derived at the PDA itself, as opposedto being derived from processing of the PSA intensity value outputs,e.g., by incorporating a digital signal processor (“DSP”) in the PDA,which may, e.g., be specifically programmed and perhaps have specializedarithmetic or algebraic or trigonometric or the like circuitry forprocessing certain aspects of conversion of, e.g., PDA intensity valuesinto a w₁ and a w₂ in the form of an FWXM or EX as a real time output ofthe bandwidth detector apparatus and associated circuitry. Subsequentprocessing of, e.g., the pertinent equation for determining the actualparameter desired may then occur in a separate processor or perhaps alsoon the DSP itself. More granularity can be added to the bandwidthdetector output in terms of, e.g., increasing the number of pixels(diodes) in the array to both speed processing and increase SNR. Otherchanges and modification may also be made within the scope of theappended claims and the present invention should be interpreted in scopesolely from such claims.

Additionally, the embodiments described involve multivariable linearequations, however, those skilled in the art will appreciate that theremay be instances where nonlinear terms may appear in the translationfunction containing the calibration coefficients. Also, the embodimentshave been described in relation to bandwidths of laser output light ofrelatively narrow bandwidth, e.g., for lithography uses. However, forother light sources where narrow bandwidth determination may berequired, e.g., EUV light sources and using similar or other forms ofmonochromatography where similar inaccuracies are introduces in themeasurements due to instrument characteristics, the present inventionmay also be utilized. Furthermore, some details have been given as tothe determination of the calibration coefficients, but it will also beunderstood by those skilled in the art that some measurement of actualbandwidth as determined by a so-called “trusted standard” correlatedagainst the occurrence of the two values of the first and secondbandwidth monitor outputs can be made with the application of well knownand understood standard error propagation techniques. What is requiredfor the performance (accuracy) of a “trusted standard” is that therandom errors of the trusted standard, as determined using errorpropagation techniques, e.g., as set out in Berington, Data Reductionand Error Analysis for the Physical Sciences, must be of the same orderor less than the random errors for the, e.g., etalon measurements fromthe bandwidth monitor that are propagated through the multivariabletransformation equation (s)

1. A bandwidth meter for measuring the bandwidth of a spectrum of lightemitted from a laser input to the bandwidth meter comprising: an opticalbandwidth monitor providing a first output representative of a firstparameter which is indicative of the bandwidth of the light emitted fromthe laser and a second output representative of a second parameter whichis indicative of the bandwidth of the light emitted from the laser; and,an actual bandwidth calculation apparatus utilizing the first output andthe second output as part of a multivariable equation employingpredetermined calibration variables specific to the optical bandwidthmonitor, to calculate an actual bandwidth parameter.
 2. The apparatus ofclaim 1 further comprising: the actual bandwidth parameter is a spectrumfull width at some percent of the maximum within the full width of thespectrum of light emitted from the laser (“FWXM”).
 3. The apparatus ofclaim 1, further comprising: the actual bandwidth parameter is a widthbetween two points on the spectrum defining a content of the spectrumenclosing some percentage of the energy of the full spectrum of thespectrum of light emitted from the laser (“EX”).
 4. The apparatus ofclaim 1 further comprising: the bandwidth monitor is an etalon and thefirst output is representative of at least one of a width of a fringe ofan optical output of the etalon at FWXM or a width between two points onthe spectrum enclosing some percentage of the energy of the fullspectrum of light emitted from the laser (“EX′”) and the second outputis representative of at least one of a second FWX″M or EX′″, where X≠X″and X′≠X′″.
 5. The apparatus of claim 1, further comprising: theprecomputed calibration variables are derived from a measurement of thevalue of the actual bandwidth parameter utilizing a trusted standard,correlated to the occurrence of the first and second outputs for acalibration spectrum.
 6. The apparatus of claim 1, further comprising:the value of the actual bandwidth parameter is calculated from theequation: estimated actual BW parameter=K*w₁+L*w₂+M, where w₁=the firstmeasured output representative of FWXM or EX′ and w₂ is the secondmeasured output representative of FWX″M or EX′″.
 7. The apparatus ofclaim 5, further comprising: the value of the actual bandwidth parameteris calculated from the equation: estimated actual BWparameter=K*w₁+L*w₂+M, where w₁=the first measured output representativeof FWXM or EX′ and w₂ is the second measured output representative ofFWX″M or EX′″.
 8. A photolithography light source comprising: abandwidth meter for measuring the bandwidth of a spectrum of lightemitted from a laser input to the bandwidth meter comprising: an opticalbandwidth monitor providing a first output representative of a firstparameter which is indicative of the bandwidth of the light emitted fromthe laser and a second output representative of a second parameter whichis indicative of the bandwidth of the light emitted from the laser; and,an actual bandwidth calculation apparatus utilizing the first output andthe second output as part of a multivariable equation employingpredetermined calibration variables specific to the optical bandwidthmonitor, to calculate an actual bandwidth parameter.
 9. The apparatus ofclaim 8 further comprising: the actual bandwidth parameter is a spectrumfull width at some percent of the maximum within the full width of thespectrum of light emitted from the laser (“FWXM”).
 10. The apparatus ofclaim 8, further comprising: the actual bandwidth parameter is a widthbetween two points on the spectrum enclosing some percentage of theenergy of the full spectrum of the spectrum of light emitted from thelaser (“EX”).
 11. The apparatus of claim 8 further comprising: thebandwidth monitor is an etalon and the first output is representative ofat least one of a width of a fringe of an optical output of the etalonat FWXM or a width between two points on the spectrum enclosing somepercentage of the energy of the full spectrum of light emitted from thelaser (“EX′”) and the second output is representative of at least one ofa second FWX″M or EX′″, where X≠X″ and X′≠X′″.
 12. The apparatus ofclaim 8, further comprising: the precomputed calibration variables arederived from a measurement of the value of the actual bandwidthparameter utilizing a trusted standard, correlated to the occurrence ofthe first and second outputs for a calibration spectrum.
 13. Theapparatus of claim 8, further comprising: the value of the actualbandwidth parameter is calculated from the equation: estimated BWparameter=K*w₁+L*w₂+M, where w₁=the first measured output representativeof FWXM or EX′ and w₂ is the second measured output representative ofFWX″M or EX′″.
 14. The apparatus of claim 12, further comprising: thevalue of the actual bandwidth parameter is calculated from the equation:estimated BW parameter=K*w₁+L*w₂+M, where w₁=the first measured outputrepresentative of FWXM or EX′ and w₂ is the second measured outputrepresentative of FWX″M or EX′″.
 15. A photolithography light sourcecomprising: a bandwidth meter for measuring the bandwidth of a spectrumof light emitted from a laser input to the bandwidth meter comprising:an optical bandwidth monitor providing a first output representative ofa first spectrum width measurement as measured by the bandwidth monitorand a second spectrum width measurement measured by the opticalbandwidth monitor; and, an actual bandwidth calculation apparatusutilizing the first output and the second output as part of amultivariable equation employing predetermined calibration variablesspecific to the optical bandwidth monitor, to calculate an actualbandwidth parameter.
 16. The apparatus of claim 15 further comprising:the actual bandwidth parameter is a spectrum full width at some percentof the maximum within the full width of the spectrum of light emittedfrom the laser (“FWXM”).
 17. The apparatus of claim 15, furthercomprising: the actual bandwidth parameter is a width between two pointson the spectrum enclosing some percentage of the energy of the fullspectrum of the spectrum of light emitted from the laser (“EX”).
 18. Theapparatus of claim 15 further comprising: the bandwidth monitor is anetalon and the first output is representative of at least one of a widthof a fringe of an optical output of the etalon at FWXM or a widthbetween two points on the spectrum enclosing some percentage of theenergy of the full spectrum of light emitted from the laser (“EX′”) andthe second output is representative of at least one of a second FWX″M orEX′″, where X≠X″ and X′≠X′″.
 19. The apparatus of claim 15, furthercomprising: the precomputed calibration variables are derived from ameasurement of the value of the actual bandwidth parameter utilizing atrusted standard, correlated to the occurrence of the first and secondoutputs for a calibration spectrum.
 20. The apparatus of claim 15,further comprising: the value of the actual bandwidth parameter iscalculated from the equation: estimated BW parameter=K*w₁+L*w₂+M, wherew₁=the first measured output representative of FWXM or EX′ and w₂ is thesecond measured output representative of FWX″M or EX′″.
 21. Theapparatus of claim 19, further comprising: the value of the actualbandwidth parameter is calculated from the equation: estimated BWparameter=K*w₁+L*w₂+M, where w₁=the first measured output representativeof FWXM or EX′ and w₂ is the second measured output representative ofFWX″M or EX′″.
 22. A photolithography light source comprising: abandwidth meter for measuring the bandwidth of a spectrum of lightemitted from a laser input to the bandwidth meter comprising: an opticalbandwidth monitor providing a first output representative of a firstspectrum width measurement as measured by the optical bandwidth detectorand a second spectrum width measurement measured by the opticalbandwidth detector; and, an actual bandwidth calculation apparatusutilizing the first output and the second output as part of amultivariable equation employing predetermined calibration variablesspecific to the optical bandwidth monitor, to calculate an actualbandwidth parameter.
 23. The apparatus of claim 22 further comprising:the actual bandwidth parameter is a spectrum full width at some percentof the maximum within the full width of the spectrum of light emittedfrom the laser (“FWXM”).
 24. The apparatus of claim 22, furthercomprising: the actual bandwidth parameter is a width between two pointson the spectrum enclosing some percentage of the energy of the fullspectrum of the spectrum of light emitted from the laser (“EX”).
 25. Amethod for measuring the bandwidth of a spectrum of light emitted from alaser input to the bandwidth meter comprising: utilizing an opticalbandwidth monitor, providing a first output representative of a firstparameter which is indicative of the bandwidth of the light emitted fromthe laser and a second output representative of a second parameter whichis indicative of the bandwidth of the light emitted from the laser; and,in an actual bandwidth calculation apparatus, utilizing the first outputand the second output as part of a multivariable linear equationemploying predetermined calibration variables specific to the opticalbandwidth monitor, calculating an actual bandwidth parameter.